It should be possible in theory, in the exact same way it is possible to disable the other buttons - but I don't know its designation. You might want to experiment or wait for someone who's more knowledgeable than me to come.
In the meantime, you can disable the the stick's touch input - either via Tincore (mapping it to blank) or via the JXD mapper (via a tick box). For the emulators and system menus that natively support hardware buttons it will not be enough and may require setting keys manually, but it will solve some of the issues you're having.
Checking my own device, if you're continuously pressing up on the joystick it's registered as only a single key stroke in most menus - so it might not be a bad solution after all.
